Question

Which of the following images represents the polar graph of r = 4sin 2θ?

Answer 1

In this problem, we want to determine the graph of a polar equation.

We are given the following polar equation:

`r=4\sin2\theta`

The general form for this polar equation is a rose curve:

`r=a\sin n\theta`

We know the following rules:

• When n is an even number, there are 2n petals

,

• The value of a gives us the length of the petals.

Since we are working with a sine function, the petals will not aline with the x and y axis, as the sine function begins at the origin.

So we know the following:

`\begin{gathered} r=4\sin2\theta \\ \\ a=4 \\ \\ n=2 \end{gathered}`

The length of our petals is 4 units, and there will be a total of 4 petals.

Here's the graph: